http://www.ck12.org Chapter 15. Concepts of Statistics
TABLE15.4:
Outcome 31 35 37 39 43 47 49
Probability 0.1 0.1 0.1 0.2 0.2 0.2 0.1- Every day you record about how long it takes to get to school.
TABLE15.5:
Time Number of Days
5-7 minutes 1
7-8 minutes 4
8-9 minutes 7
9-10 minutes 9
10-12 minutes 2How long does it take you to get to school on average?
Answers:
- 0· 0. 935 + 5 · 0. 04 + 10 · 0. 02 + 30 · 0. 005 − 1 =− 0. 45 .You will lose $0.45 on average if you play the slot machine
many times. - 31· 0. 1 + 35 · 0. 1 + 37 · 0. 1 + 39 · 0. 2 + 43 · 0. 2 + 47 · 0. 2 + 49 · 0. 1 = 41
- To answer this question, you could find the weighted average of the expected value. If you choose expected value,
consider that the situation gives you frequency rather than probability. You can calculate the probability of each of
the categories by dividing each frequency by the total number of days (23). Since the time occurs in intervals, it is
reasonable to use the average time in each interval as representative of the category when calculating the expected
value.
TABLE15.6:
Time Number of Days Probability
5-7 minutes 1 231
7-8 minutes 4 234
8-9 minutes 7 237
9-10 minutes 9 239
10-12 minutes 2 2326 · 231 + 7. 5 · 234 + 8. 5 · 237 + 9. 5 · 239 + 11 · 232 =^20323 ≈ 8. 8
On average, it takes you 8-9 minutes to get to school.
Practice
- Explain how to calculate expected value.
- True or false: If the expected value of a game is $0.50, then you can expect to win $0.50 each time you play.
- True or false: The greater the number of games played, the closer the average winnings will be to the theoretical
expected value. - A player rolls a standard pair of dice. If the sum of the numbers is a 6, the player wins $6. If the sum of the
numbers is anything else, the player has to pay $1. What is the expected value for this game?